I understand that according to Einstein's Special Theory of Relativity
(which concerns bodies moving at a constant speed) it is not possible
to say what the absolute speed of any body is. Only its speed relative
to another body can be determined. For example, if a car is, according
to the usual way to viewing matters, travelling at 20mph relative to
the road, it would be equally valid to say that the car is stationary
and that the road is travelling at 20 mph relative to the car.

My question is, does this principle also hold good in the case of
angular motion? For example, instead of saying that the earth rotates
on its axis once every 24 hours (relative to the stars) would it be
equally valid to say that the stars orbit the earth one every 24 hours
relative to the earth?

If this would not be an equally valid way of looking at it, why not?

If this would be an equally valid way of looking at it, does that mean
that the stars which orbit the earth are necessarily (from this frame
of reference) travelling faster than the speed of light? If not why
not?

The answer given above is incorrect. While the theory of special
relativity tells us that all inertial reference frames are equivalent,
this equivalence does not hold for rotational reference frames.
Constant rotational motion requires a constant acceleration, and
acceleration is something you can measure without ambiguity, unlike
velocity which is defined only with respect to a given reference
frame.

And no, it is never true that the relative velocity of two ships
exceeds the speed of light. If two ships are on a collision course,
and each of them is traveling 3/4 the speed of light relative to the
fixed ocean, their relative velocity still does not exceed the speed
of light. At such speeds, one cannot simply add the two velocities;
instead one must use the velocity addition formula from the theory of
special relativity. For details, see (for instance)

http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html

If you want to understand--*really* understand-- why the laws of
physics are not the same in rotating reference frames, go to your
local playground and try some simple physics experiments on the
merry-go-round.

The answer is indeed incorrect  as pointed out in the comment.
The point which also should be made is that rotation is not described
 by special relativity.

 When we apply general realtivity, the apearance of centrifugal force
does not
 contradict the relativity, as commenter suggest.
 That is actually meaning of the principle of
 equivalence.  An observer in closed box cannot tell the difference
 between being accelerated or sitting in gravitaonal field. 
 
 That is true locally (box is small - a point in fact).  When you
apply it to
 universe - it becomes very complicated and one has to consider
cosmological
models.  The equations of general relativity are covariant (which is
one way to
 make meaning of 'relative' more precise, but there is no real motion
which would look
 like a gravity of a star.

 So answer is sort of yes and no and physicstt are still arguing bout
weak and strong
 Principle of Equivalence. 

Either way, it is a good question and shows good physics intuition,
which desreves better answers thanyou got so far.
Pick up a good book.

Hi,
I think your understanding of the Special Theory of Relativity is off
by just a little.  You say that it "concerns bodies moving at a
constant speed."  This isn't quite right.  The Special Theory of
Relativity concerns bodies moving at a constant velocity.  Velocity
takes into account both speed and direction of travel while speed says
nothing about the direction.  So to have constant velocity, both the
speed and the direction of travel have to be constant.  This is
basically the same as saying that the object has zero acceleration. 
With angular motion the direction is always changing.  This means that
even if the speed is constant there is still acceleration.  This also
means that you cannot use the Special Theory, you must instead use the
General Theory of Relativity.

analogkid

"Since I posted my original question, I can see that my reference to
Special Relativity could be confusing. The Google Answers systems does
not allow me to actually edit my original question but please imagine
that the following paragraph is inserted between the first and second
paragraphs of my original question:

In the General Theory of Relativity (which, unlike the Special Theory,
also covers bodies not moving at a constant velocity) there is the
Principle of Equivalence according to which, for example, the force
felt by astronauts in an rocket in interstellar space which is held to
be caused by the acceleration of the rocket in a certain direction,
could with equal validity be accounted for by the gravitational field
on the assumption that the rocket is stationary (or travelling at a
constant velocity) and the stars are accelerating in the opposite
direction."